### Abstract

The Phelps-Koopmans theorem states that if every limit point of a path of capital stocks exceeds the "golden rule," then that path is inefficient: there is another feasible path from the same initial stock that provides at least as much consumption at every date and strictly more consumption at some date. I show that in a model with nonconvex technologies and preferences, the theorem is false in a strong sense. Not only can there be efficient paths with capital stocks forever above and bounded away from a unique golden rule, such paths can also be optimal under the infinite discounted sum of a one-period utility function. The paper makes clear, moreover, that this latter criterion is strictly more demanding than the efficiency of a path.

Original language | English (US) |
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Pages (from-to) | 11-28 |

Number of pages | 18 |

Journal | International Journal of Economic Theory |

Volume | 6 |

Issue number | 1 |

DOIs | |

State | Published - 2010 |

### Keywords

- Dynamic optimization
- Efficiency
- Nonconvexities
- Phelps-koopmans theorem

### ASJC Scopus subject areas

- Economics and Econometrics

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## Cite this

*International Journal of Economic Theory*,

*6*(1), 11-28. https://doi.org/10.1111/j.1742-7363.2009.00119.x